# Direct Diffusion Bridge using Data Consistency for Inverse Problems

arXiv: https://arxiv.org/abs/2305.19809 · HTML: https://mlsanity.com/paper/2305.19809/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 31 of its 43 references that are in the map.
- First posted on arXiv 31 May 2023.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Solving 3D Inverse Problems using Pre-trained 2D Diffusion Models](https://mlsanity.com/paper/2211.10655/) (2022)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [CNN-Based Projected Gradient Descent for Consistent Image Reconstruction](https://mlsanity.com/paper/1709.01809/) (2017)

## Built on by (most cited first, 30 of 66)

- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [Diffusion Models in Low-Level Vision: A Survey](https://mlsanity.com/paper/2406.11138/) (2024)
- [Self-Consistent Recursive Diffusion Bridge for Medical Image Translation](https://mlsanity.com/paper/2405.06789/) (2024)
- [SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems](https://mlsanity.com/paper/2410.04479/) (2024)
- [OFTSR: One-Step Flow for Image Super-Resolution with Tunable Fidelity-Realism Trade-offs](https://mlsanity.com/paper/2412.09465/) (2024)
- [Augmented Bridge Matching](https://mlsanity.com/paper/2311.06978/) (2023)
- [Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problems](https://mlsanity.com/paper/2406.02462/) (2024)
- [Diffusion models for inverse problems](https://mlsanity.com/paper/2508.01975/) (2025)
- [Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstruction](https://mlsanity.com/paper/2308.14409/) (2023)
- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [Implicit Image-to-Image Schrodinger Bridge for Image Restoration](https://mlsanity.com/paper/2403.06069/) (2024)
- [Diffusion State-Guided Projected Gradient for Inverse Problems](https://mlsanity.com/paper/2410.03463/) (2024)
- [Rethinking Visual Counterfactual Explanations Through Region Constraint](https://mlsanity.com/paper/2410.12591/) (2024)
- [Audio Super-Resolution with Latent Bridge Models](https://mlsanity.com/paper/2509.17609/) (2025)
- [Adversarial Schr"odinger Bridge Matching](https://mlsanity.com/paper/2405.14449/) (2024)
- [DiffusionBlend: Learning 3D Image Prior through Position-aware Diffusion Score Blending for 3D Computed Tomography Reconstruction](https://mlsanity.com/paper/2406.10211/) (2024)
- [CoSIGN: Few-Step Guidance of ConSIstency Model to Solve General INverse Problems](https://mlsanity.com/paper/2407.12676/) (2024)
- [Diffusion Prior-Based Amortized Variational Inference for Noisy Inverse Problems](https://mlsanity.com/paper/2407.16125/) (2024)
- [Invertible Diffusion Models for Compressed Sensing](https://mlsanity.com/paper/2403.17006/) (2024)
- [Generalized Consistency Trajectory Models for Image Manipulation](https://mlsanity.com/paper/2403.12510/) (2024)
- [Think Twice Before You Act: Improving Inverse Problem Solving With MCMC](https://mlsanity.com/paper/2409.08551/) (2024)
- [Patch-Based Diffusion Models Beat Whole-Image Models for Mismatched Distribution Inverse Problems](https://mlsanity.com/paper/2410.11730/) (2024)
- [Solving Inverse Problems via Diffusion Optimal Control](https://mlsanity.com/paper/2412.16748/) (2024)
- [FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems](https://mlsanity.com/paper/2411.18970/) (2024)
- [DPBridge: Latent Diffusion Bridge for Dense Prediction](https://mlsanity.com/paper/2412.20506/) (2024)
- [Learning few-step posterior samplers by unfolding and distillation of diffusion models](https://mlsanity.com/paper/2507.02686/) (2025)
- [Cross-view Generalized Diffusion Model for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2508.10313/) (2025)
- [Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamics](https://mlsanity.com/paper/2406.13652/) (2024)
- [Learning Efficient and Effective Trajectories for Differential Equation-based Image Restoration](https://mlsanity.com/paper/2410.04811/) (2024)

## Abstract (arXiv)

Diffusion model-based inverse problem solvers have shown impressive performance, but are limited in speed, mostly as they require reverse diffusion sampling starting from noise. Several recent works have tried to alleviate this problem by building a diffusion process, directly bridging the clean and the corrupted for specific inverse problems. In this paper, we first unify these existing works under the name Direct Diffusion Bridges (DDB), showing that while motivated by different theories, the resulting algorithms only differ in the choice of parameters. Then, we highlight a critical limitation of the current DDB framework, namely that it does not ensure data consistency. To address this problem, we propose a modified inference procedure that imposes data consistency without the need for fine-tuning. We term the resulting method data Consistent DDB (CDDB), which outperforms its inconsistent counterpart in terms of both perception and distortion metrics, thereby effectively pushing the Pareto-frontier toward the optimum. Our proposed method achieves state-of-the-art results on both evaluation criteria, showcasing its superiority over existing methods. Code is available at https://github.com/HJ-harry/CDDB